# A ranger spots a forest fire while on a 60-meter observation tower. The angle of depression from the tower to the fire is 25°. To the nearest meter, how far is the fire from the base of the tower?

Apr 25, 2018

$\frac{60}{\tan {25}^{\circ}} \approx 129$ meters
We have a right triangle with the horizontal part as the unknown $x ,$ the vertical part $60$ meters and the hypotenuse our line of sight, which makes a ${25}^{\circ}$ angle to the horizontal.
$\tan {25}^{\circ} = \frac{60}{x}$
$x = \frac{60}{\tan {25}^{\circ}} \approx 128.67$ which is $129$ meters after rounding.